The polar curve and speed-to-fly

On one of your first high flights it will happen: the landing field (LZ) lies upwind, and it looks further away than it should. Every instinct says slow down and stretch the glide. On a paraglider that instinct is wrong, and this lesson shows why with one simple graph.

The graph is the speed polar. It sums up how your wing flies, and once you can read it, three everyday decisions make sense: hands up most of the time, a little brake in lift (rising air), and more speed into wind and through sinking air.

What the polar shows

The polar shows how fast the wing sinks at each steady airspeed in still air¹. Airspeed runs across the page; sink rate runs down. Each point on the curve is one way of flying it: a hand position on the brakes, or a push on the speed bar.

Figure: Read the curve from left to right: the stall, the back side, minimum sink, hands up (about best glide here) and full speed bar. A reference school wing: the dashed ends are estimates, and your wing will differ.

Five points worth knowing

“Light brake” for minimum sink means hands between shoulder and eye height on one school wing, or about 20 cm7.9 in of brake on another⁵. Certificate stickers declare about 13–14 km/h8–9 mph of speed range on the brakes alone and 21–23 km/h13–14 mph in total with the bar⁸. Every wing differs: check your manual.

The back side

Between the stall and minimum sink lies the back side of the curve. Here, flying slower makes you sink faster as well as go slower¹, so there is nothing to gain and the stall is close. You feel it: the brake pressure rises and the wind noise fades⁶.

Glide ratio: a line from the origin

Glide ratio is how far you go forward for each metre of height you lose. In still air it equals the wing’s lift-to-drag ratio, and it is also forward speed divided by sink rate⁹. BGD gives 8.5:1 for its school wing at a trim of about 37 km/h23 mph, roughly 10 m/s1,960 ft/min forward, which means sinking about 1.2 m/s240 ft/min³⁶.

On the polar, a straight line from the origin to a point on the curve shows the glide at that speed: the steeper the line, the more height you lose for each metre forward, so the worse the glide. Swing a line down from the origin until it just touches the curve: that touching point is best glide¹.

On school wings best glide sits at or very near trim speed, so hands up is also your best still-air glide⁶. Minimum sink, a little slower, glides slightly less far. Makers’ glide figures are not directly comparable: one manufacturer publishes none, because harness and sitting position alone can change the glide by up to a whole point¹⁰.

Speed-to-fly

Best glide is best only in still air. The speed-to-fly is the airspeed that gives the flattest glide over the ground in the air you are actually in. The rule:

• into a headwind or through sink, fly faster¹¹¹²;
• with a tailwind, fly a little slower, but never below minimum sink¹¹; in rising air, slow toward minimum sink, which is light brake⁵.

Why faster into wind? Every second in the air costs height while the wind pushes you back, so a faster glide spends fewer seconds per metre of ground. Your groundspeed is your airspeed minus the headwind; when the headwind equals your airspeed you stand still, and a stronger one carries you backwards¹³. In sinking air the logic is the same: get through it quickly.

The polar shows how much faster. Move the starting point of the tangent right by the headwind (left for a tailwind) and up by the sinking air. The new tangent touches the curve at the speed-to-fly¹¹.

Figure: Move the wind and air sliders and watch the tangent. In still air it touches at about trim speed: hands up. The slow and fast ends of this reference curve and the hand positions are estimates, so treat those numbers as rough.

Into a headwind

Into a headwind, speeding up wins ground you would otherwise lose. The figure below uses the same school wing from 100 m330 ft.

Figure: Into wind the slowest speed lands far shorter; downwind the three land close together. Distances are rounded, and the slow and fast cases rest on estimated parts of the curve.

In practice: hands fully up first, then the speed bar if your instructor has trained you and conditions allow¹². The bar lowers the angle of attack, so the wing collapses more easily: avoid it near the ground and in turbulence, and only fly where you can make progress into wind without it¹⁴. Never brake while on the bar; if the wing collapses or the air turns rough, release the bar first¹⁵. Speed bar and big ears covers the technique.

Downwind

With a tailwind the wind does the work, and the speed you choose barely matters. A touch of brake gains a little, but never slow down because the ground is rushing past: wind changes your groundspeed, not your airspeed¹⁶, and pilots who brake to slow down downwind can stall¹⁷.

In sink and in lift

In sinking air, speed up to spend less time in it¹¹. In rising air, slow toward minimum sink: it is the lowest sink rate your wing has, so it gives the best climb¹. When the air rises faster than your minimum sink rate, you climb¹⁸.

Weight and altitude

Wing loading slides the whole polar. Heavier, the same wing flies faster at every point and sinks correspondingly faster, but its best glide ratio stays the same¹⁹²⁰. Near the top of the weight range it penetrates wind better but damps itself less; near the bottom it is slower and sinks a little less, though it deforms more easily in strong turbulence²¹. See certification and sizing, and try the weight slider in the explorer.

Altitude does something similar. In thin, high or hot air the wing flies faster through the air for the same feel, about 2% for every 300 m985 ft²², with the same glide ratio¹⁹²³; you also land faster on a high field.

Choosing your speed in flight